FOM: Philosophy and platonism

Martin Davis martin at
Sun Jan 23 14:05:13 EST 2000

At 12:09 AM 1/23/00 +0200, Mark Steiner wrote:

>I'm not disparaging the worth of other books on this question like those 
>of Field, Maddy, Shapiro, Azzouni, Balaguer, Resnik, Hale, Katz, Chihara, 
>and others, which take
>particular stands on the question.

My reading in this area has certainly been casual. However, I'd like to say 
that I'm a great fan of Maddy whose stance of beginning with what 
mathematicians actually DO strikes me as exactly right. Balaguer's book, 
"Platonism and Anti-Platonism in Mathematics", on the other hand, is an 
example of the kind of writing by philosophers on f.o.m. guaranteed to put 
mathematicians off.

Foundational issues reach the consciousness of mathematicians when they 
have impact on mathematical practice. (And I firmly believe that for work 
on these issues to have importance, they need to be focused in just this 
manner.) Historical examples could easily be given. Today the issues 
staring workers in f.o.m. in the face relate to making sense of large 
cardinal axioms. This includes the work on determinancy: Martin, Steel, 
Woodin, and the use of such axioms to go beyond ZFC in obtaining arithmetic 
theorems as particularly in the work of Friedman.


                           Martin Davis
                    Visiting Scholar UC Berkeley
                      Professor Emeritus, NYU
                          martin at
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